The Probabilistic Method (PDF)

The leading reference on probabilistic methods in combinatorics-now
expanded and updated

When it was first published in 1991, The Probabilistic Method
became instantly the standard reference on one of the most powerful
and widely used tools in combinatorics. Still without competition
nearly a decade later, this new edition brings you up to speed on
recent developments, while adding useful exercises and over 30% new
material. It continues to emphasize the basic elements of the
methodology, discussing in a remarkably clear and informal style
both algorithmic and classical methods as well as modern
applications.

The Probabilistic Method, Second Edition begins with basic
techniques that use expectation and variance, as well as the more
recent martingales and correlation inequalities, then explores
areas where probabilistic techniques proved successful, including
discrepancy and random graphs as well as cutting-edge topics in
theoretical computer science. A series of proofs, or "probabilistic
lenses," are interspersed throughout the book, offering added
insight into the application of the probabilistic approach. New and
revised coverage includes:

* Several improved as well as new results

* A continuous approach to discrete probabilistic problems

* Talagrand's Inequality and other novel concentration
results

* A discussion of the connection between discrepancy and
VC-dimension

* Several combinatorial applications of the entropy function and
its properties

* A new section on the life and work of Paul Erdös-the
developer of the probabilistic method